Infinite mixture of piecewise linear sequences

Abstract

In this paper, we present an infinite mixture model to partition short time series data. Components of this mixture model are piecewise linear sequences. The model is constructed using Chinese restaurant process and the posterior distribution over the sample assignments are calculated using collapsed Gibbs sampling. A piecewise linear sequence is represented by fewer parameters than its observations. Thus, the mean parameter of the likelihood is obtained by applying a matrix transformation on the component parameters. This matrix is constructed by a special method according to the rules that define our piecewise linear sequences.